erdos_252.prime_tuples

If the prime `k`-tuples conjecture is true, then `∑ σ k n / n!` is irrational. This is proved in [FLC07].

theorem erdos_252.prime_tuples {k : ℕ} (hk : 4 ≤ k) (hp : ∀ (a : Fin k → ℕ+) (b : Fin k → ℕ)
    (hab : ∀ p, p.Prime → ∃ n, ¬ p ∣ ∏ i, (a i * n + b i)),
    Set.Infinite {n | ∀ i : Fin k, (a i * n + b i).Prime} ) :
    Irrational (∑' n, σ k n / (n ! : ℝ))

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